Methods

Objective

In this project my objective was to find patterns in past or current loans that might be correlated with successful completion or default of a current loan. To this end I divided the loans into two groups, the “Completed”/“Defaulted” and the “Current”, and I investigated these two groups separately. In used univariate analysis to get a better sense of the dataset and multivariate analysis, along with statistical tests when necessary, to uncover possible correlations. Finally, I focused my analysis, in most parts, on those individuals that I considered as more prone to default.

Dataset

I investigated the Loan Data from Prosper. As the description in the project page states this data set contains 113,937 loans with 81 variables on each loan, including loan amount, borrower rate (or interest rate), current loan status, borrower income, borrower employment status, borrower credit history, and the latest payment information.

The main variables which I explored were:

1. LoanStatus
2. EmploymentStatus
3. CurrentDelinquencies
4. DelinquenciesLast7Years
5. AmountDelinquent
7. AvailableBankcardCredit
8. DebtToIncomeRatio
9. IncomeRange
10. StatedMonthlyIncome
11. LoanCurrentDaysDelinquent
12. LoanOriginalAmount
13. MonthlyLoanPayment

Results

Population characteristics

The total population is 113,937 individuals

n <- length(loans$ListingKey)
n
## [1] 113937

First I wanted to investigate the LoanStatus variable. For higher clarity of the bar plot, below I printed the four most frequent values:

1. Chargedoff
2. Completed
3. Current
4. Defaulted

We see that current and completed loans consist the majority of the data.

##              Cancelled             Chargedoff              Completed 
##                      5                  11992                  38074 
##                Current              Defaulted FinalPaymentInProgress 
##                  56576                   5018                    205 
##   Past Due (>120 days)   Past Due (1-15 days)  Past Due (16-30 days) 
##                     16                    806                    265 
##  Past Due (31-60 days)  Past Due (61-90 days) Past Due (91-120 days) 
##                    363                    313                    304

Here we can see that about 50% of the individuals are homeowners.

summary(loans$IsBorrowerHomeowner)
## False  True 
## 56459 57478

Here I plotted the employment status of the individuals. From the subsequent analysis I excluded those with employment status either empty or not available.

##                    Employed     Full-time Not available  Not employed 
##          2255         67322         26355          5347           835 
##         Other     Part-time       Retired Self-employed 
##          3806          1088           795          6134

Here we see the number of delinquencies for the individuals (current and total in 7 years). The majority of the population never had any delinquencies (about 67%), while about 79% of the population doesn’t currently have any delinquencies.

Since the majority in both cases is zero, we only show those that have or had at least one delinquency. Both plots are in the same scale for easier comparison.

summary(loans$CurrentDelinquencies)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##  0.0000  0.0000  0.0000  0.5921  0.0000 83.0000     697
zero_current_delinquencies <- subset(loans$CurrentDelinquencies, 
                                       loans$CurrentDelinquencies == 0)
length(zero_current_delinquencies)
## [1] 89742
summary(loans$DelinquenciesLast7Years)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##   0.000   0.000   0.000   4.155   3.000  99.000     990
zero_total_delinquencies <- subset(loans$DelinquenciesLast7Years, 
                                       loans$DelinquenciesLast7Years == 0)
length(zero_total_delinquencies)
## [1] 76439

There are a lot of individuals with a delinquent amount minor or equal to zero. Here I wanted to see the distribution for those that have delinquent amounts higher than 10,000 dollars (2,584 individuals) and thus they might be more prone to default. Below we also see a summary of the results.

summary(loans$AmountDelinquent)
##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max.     NA's 
##      0.0      0.0      0.0    984.5      0.0 463900.0     7622
high_delinquency <- 10000
high_delinquency_individuals <- subset(loans$AmountDelinquent, 
                                       loans$AmountDelinquent > high_delinquency)
length(high_delinquency_individuals)
## [1] 2584
summary(high_delinquency_individuals)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   10010   13430   19660   31170   33560  463900

Here I show the available bank card credit. My interest is to see beter those with the lowest credit, so I plotted only those with less than 50,000.

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##       0     880    4100   11210   13180  646300    7544

Here I wanted to look more into those with the highest exposure (debt 50% or higher than their income). We see that there is an unexpected peak at 10.0. That point either is an error or it refers to all those that have debt to income ratio higher than 10.0.

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##   0.000   0.140   0.220   0.276   0.320  10.010    8554

The income range of the individuals.

##             $0      $1-24,999 $25,000-49,999 $50,000-74,999 $75,000-99,999 
##            621           7274          32192          31050          16916 
##      $100,000+   Not employed  Not displayed 
##          17337            806           7741

Again I wanted to look more in detail on those with less income. For instance, those with yearly income less than 50,000. Intrestignly there is a peak in zero. These people are eiher not reporting their income correctly or they are funded from someone else.

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##       0    3200    4667    5608    6825 1750000

Loan current days delinquent (more than 0 days).

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##     0.0     0.0     0.0   152.8     0.0  2704.0

Loan original amount. The peaks in the histogram are due to the fact that people tend to loan well rounded amounts.

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1000    4000    6500    8337   12000   35000

Monthly loan payment (greater than 0).

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##     0.0   131.6   217.7   272.5   371.6  2252.0

Finished loans

In this section, I explored the relationship of the “Completed” and “Defaulted” loans, with their respective loantakers’ employment status and other parameters. I analyzed those with loan status completed or defaulted to see whether I could find patterns that would allow me to predict what will happen with those still repaying their loans.

First, I investigated the total delinquencies for the last 7 years. I excluded from the analysis all individuals with zero delinquencies. We can see that in most of the cases the median values for both completed and defaulted loans are identical. Only in the “Not employed” category the median delinquencies for the defaulted seem to differ a lot from the completed. In order to evaluate whether this difference is significant I ran a t-test. The resulting p-value is 0.56, thus I failed to reject the null hypothesis.

## 
##  Welch Two Sample t-test
## 
## data:  loans.not_employed_com$DelinquenciesLast7Years and loans.not_employed_def$DelinquenciesLast7Years
## t = -0.61616, df = 5.1074, p-value = 0.5642
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -8.501150  5.196984
## sample estimates:
## mean of x mean of y 
##  8.947917 10.600000

Next, I looked at the original amount of loaned money. In the same way, medians apeared to be very similar apart from the “Self-employed” category. For that category I performed again a t-test to see whether the difference was statistically significant. The resulting p-value was << 0.001, thus the difference is statistically significant. So self employed individuals who defaulted, took bigger loans than those who didn’t default.

## 
##  Welch Two Sample t-test
## 
## data:  loans.self_employed_com$LoanOriginalAmount and loans.self_employed_def$LoanOriginalAmount
## t = -8.0962, df = 281.22, p-value = 1.729e-14
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -4927.606 -3000.126
## sample estimates:
## mean of x mean of y 
##  6334.085 10297.951

In this plot I show the stated monthly income of those with less than 50,000 dollars per year. Interestigly people with full-time employment reported having zero monthly income. This is for sure some kind of error either in the way the data was stored or reported. In this plot all the median values are very similar to each other.

Here I explored the past delinquencies along with whether the individual was a homeowner or not. I wanted to see whether possible mortgages could play any role in the likelihood to default. From the box plots we can see that both median values and variances are very simmilar for all groups. I excluded from the analysis those with zero delinquencies.

In this plot I investigated the on time prosper payments for each employment status. Again everything seems to be very similar apart from the “Not employed”. However the p-value is about 0.77 and thus this variable does not show any differences as well.

## 
##  Welch Two Sample t-test
## 
## data:  loans.not_employed_com$OnTimeProsperPayments and loans.not_employed_def$OnTimeProsperPayments
## t = -0.35613, df = 1.2291, p-value = 0.7732
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -54.53195  50.03195
## sample estimates:
## mean of x mean of y 
##     17.75     20.00

The majority of loans are 100% funded and thus I was interested to investigate those not fully funded. The “Not employed” category has clear differences between completed and defaulted loans, however the datapoints are too few to draw any statistical conclusion. For the rest of the categories either there is not a big difference between “Completed” and “Defaulted” or the “Defaulted” category is completely absent.

In terms of the number of investors in each loan, again the results are pretty similar for all categories apart from the “Self-employed”. The p-value is << 0.001 and thus we conclude that self employed with more investors were more likely to default than the rest of the self-employed.

## 
##  Welch Two Sample t-test
## 
## data:  loans.self_employed_com$Investors and loans.self_employed_def$Investors
## t = -6.9578, df = 283.39, p-value = 2.398e-11
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -86.21806 -48.19285
## sample estimates:
## mean of x mean of y 
##  106.8799  174.0854

Current loans

Here I explored the relationship of the debt to income ratio of those that currently have an active loan, with their employment status and other parameters. I divided all individuals into two groups; those with low (<= 0.5) and those with high debt to income ratio (> 0.5). I created a bucket to put these individuals into and plotted in the same style as in the previous section. In the following plots I didn’t include NA and zero values (when applicable).

In this first plot I investigated whether the current delinquencies can reveal any pattern for those currently holding a loan. The plot shows only until 15 delinquencies but all higher than zero were included in the analysis. Making a statistical t-test to all the the individuals of different employment status we find no differences in those “Employed” and “Full-time” (p > 0.5). The “Other” have a statistically significant difference (p << 0.001) and the “Retired” a significant difference of 0.01 < p < 0.05. Finally, for the “Part-time” there are not enough observations and the “Self-employed” are only in low debt to income ratio.

(Example: t-test for the “Retired”)

## 
##  Welch Two Sample t-test
## 
## data:  current_loans.employment_low$CurrentDelinquencies and current_loans.employment_high$CurrentDelinquencies
## t = 2.3041, df = 16, p-value = 0.03496
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.05642235 1.35534236
## sample estimates:
## mean of x mean of y 
##  1.705882  1.000000

Here I explored those who had delinquent amounts higher than 1,000 dollars (plot shows until 100,000 dollars but I included all higher amounts in the analysis). Those “Employed” and “Other” were similar for both bucket groups, while those “Full-time” had a statistically significant difference (p << 0.001). All the rest do not have enough observations to perform a t-test.

(Example: t-test for the “Full-time”)

## 
##  Welch Two Sample t-test
## 
## data:  current_loans.employment_low$AmountDelinquent and current_loans.employment_high$AmountDelinquent
## t = 6.1277, df = 147.38, p-value = 7.746e-09
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  10112.69 19740.29
## sample estimates:
## mean of x mean of y 
## 17728.156  2801.667

Following the observation that self employed individuals with more investors were more likely to default on their loans, I wanted to explore more that group. I looked at those currently having an active loan to see whether higher number of investors was correlated with higher debt to income ratio. The p-value of the test was >> 0.05 and thus there was no correlation. However, the retired with low debt to income ratio have a higher number of investors, which is statistically significant (0.01 > p > 0.001).

(Example: t-test for the “Retired”)

## 
##  Welch Two Sample t-test
## 
## data:  current_loans.employment_low$Investors and current_loans.employment_high$Investors
## t = 3.3541, df = 39.7, p-value = 0.001761
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  16.48478 66.50182
## sample estimates:
## mean of x mean of y 
##  70.92188  29.42857

Even though there was no correlation between the number of investors and the debt to income ratio in the self employed category, I wanted to investigate whether there were correlations with the income range instead. In the next plot I excluded the “Not employed”, the “Part-time” and the “Retired” because I wanted to focus on the rest of the categories which have more data. Below I printed how the income range is correlated with the number of investors per employment status. There are again no statistically significant differences between the groups.

(Example: t-test for the “Full-time”)

## 
##  Welch Two Sample t-test
## 
## data:  investors.income_smpl_1$Investors and investors.income_smpl_2$Investors
## t = -1.9747, df = 3.4647, p-value = 0.1304
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -137.12562   27.24842
## sample estimates:
## mean of x mean of y 
##   54.2500  109.1886

The last plot of the section shows the original amount of the loan (for those who took more than 5,000 dollars) against the same variables. In this investigation, we see that the “Employed” and the “Other” were the ones that had statistically significant differences between the bucket groups.

(Example: t-test for the “Employed”)

## 
##  Welch Two Sample t-test
## 
## data:  current_loans.employment_low$LoanOriginalAmount and current_loans.employment_high$LoanOriginalAmount
## t = 19.191, df = 1201, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  1787.741 2194.905
## sample estimates:
## mean of x mean of y 
##  13720.21  11728.88

Final plots and summary

In this section, I present the three figures that I believe are the most informative for the dataset I investigated.

Figure 1

Caption Fig. 1

This plot shows the number of investors in a finished loan, grouped by the loantakers’ employment status and coloured by the loan status. Even though most categories were equally likely to default, this plot is interesting because of the “Self-employed” category. Self employed individuals with more investors seemed to be more likely to default than the rest, which is a counterintuitive result.

Figure 2

Caption Fig. 2

In this plot we see the number of investors in a current loan, grouped by the loantakers’ employment status (excluding retired, part-time and no employed) and coloured by their income range. This plot shows that the number of investors in a loan are not dependent on the loantakers’ income (all statistical tests had p > 0.05). We saw in Fig. 1 that self employed loantakers with more investors were more likely to default. Interestigly their income is not correlated with the number of investors involved in their loan.

Figure 3

Caption Fig. 3

In this plot we see the current delinquent amounts (> 1,000 dollars) for individualts with loans, grouped by their employment status and coloured by their debt to income ratio. We can observe a statistically significant difference only in the “Full-time” status, where loantakers have lower debt to income ratio. From the “Part-time” and “Self-employed” categories we see that only those of low debt to income ratio have delinquent amounts, but they are still only a few. Also, few “Retired” people have delinquent amounts. Finally there are no significant differences in the “Employed” and “Other” groups.

Reflection

This dataset pertains to loan data for about 114,000 individuals. It contains 81 variables of which I explored around 13 of them. At first I explored the variables individually, mainly focusing on subsets of the population that I assumed to be more prone to default (low income, with delinquent payments and high debt to income ratio). Continuing, I assumed that if I explored characteristics for individuals with completed and defaulted loans, I could maybe predict whether those currently holding loans are going to default or not (only those in the category “Current” as it is the most populus).

I grouped those with completed or defaulted loans according to their employment status because I wanted to see whether this could also be a predicting factor of default. For that part of the analysis I explored variables pertaining to their delinquencies the last 7 years, original loaned amount, whether they own a home or not, investors involved etc. The first thing I observed is that there doesn’t seem to be any correlation between defaults and employment status. Furthermore, in almost all the variables I observed, both completed and defaulted loans had no statistically significant differences. Afterwards, I investigated those with loan status equal to “Current”. I wanted to see whether the currrent income, the debt to income ratio, the employment status, the loaned amount and the delinquencies will show any patterns among the population. The results of that analysis showed again no statistically significant differences in most of the values observed. From this I concluded that either there are not enough relevant variables in order to make inferences or that events which decide whether a loan defaults or not are equally possible to happen to everyone.

During the analysis it was very difficult for me to find meaningful variables to compare. As I set my goal to uncover possible driving factors that make loans default, I expected to find correlations between e.g. income or delinquent amounts and the probability for a loan to default. After extensive exploration of a lot of the variables I found only a few statistical significant differences between groups. On the one hand this was a success because these differences were very difficult to uncover, on the other hand this lack of pattern might be due to the fact that the important pieces of information responsible for the defaults are not included in this dataset. Furthermore, this dataset is limited in the sense that it doesn’t include historical data so that I could better investigate those with completed or defaulted loans at the time these loans were active. Finally, the dataset does not contain all the loans that individuals might have and it would be very interesting if these data could be compared with data from other sources to explore all possible loans for all individuals.

References

R markdown documentation: http://rmarkdown.rstudio.com/lesson-1.html

ggplot2 documentation: http://docs.ggplot2.org/current/

grid package documentation: https://stat.ethz.ch/R-manual/R-devel/library/grid/html/00Index.html